Force-sensing net

Abstract

In exemplary implementations of this invention, a basketball net or flat net measures the translational kinetic energy of a ball that passes through an aperture in the net or impacts the net. The net includes one or more electrically conductive cords, which have a resistance that varies depending on the degree to which the cord is stretched. From sensor measurements, a processor determines: (a) instantaneous rate of change of resistance, and (b) duration of a time period that begins when resistance exceeds a baseline (with hysteresis). In the case of a basketball net, a processor may calculate the translational kinetic energy of the ball as equal to a sum of two terms. The first term is inversely proportional to the square of the duration; the second is proportional to the square of the integral of the instantaneous rate of change of resistance over the time period.

What is claimed is: 
     
       1. An apparatus comprising in combination:
 (a) a net that has an aperture and that includes one or more cords, which one or more cords
 (i) are stretchable, 
 (ii) are electrically conductive, 
 (iii) have an electrical resistance that varies depending on the extent to which the one or more cords are stretched, and 
 (iv) are positioned such that the one or more cords stretch when a ball passes through the aperture; 
 
 (b) at least one sensor for measuring the electrical resistance; and 
 (c) at least one processor for performing a computation that includes
 (i) calculating a duration of a time period, which period starts when the electrical resistance exceeds a baseline plus a first amount and ends when the electrical resistance is less than the baseline minus a second amount, and 
 (ii) calculating, based at least in part on the duration of the time period, the translational kinetic energy of the ball that passes through the aperture. 
 
 
     
     
       2. The apparatus of  claim 1 , wherein the net comprises a basketball net. 
     
     
       3. The apparatus of  claim 1 , wherein the net is tubular. 
     
     
       4. The apparatus of  claim 1 , wherein the computation includes calculating an instantaneous rate of change of the resistance. 
     
     
       5. The apparatus of  claim 1 , wherein the first amount is different than the second amount. 
     
     
       6. The apparatus of  claim 1 , wherein the computation includes a mathematical operation involving a term that is inversely proportional to the square of the duration. 
     
     
       7. The apparatus of  claim 1 , wherein the computation also includes:
 (a) calculating an estimate of an integral of change in the resistance, by calculating a sum of samples; and 
 (b) calculating the translational kinetic energy as proportional to the square of the estimate of the integral. 
 
     
     
       8. The apparatus of  claim 7 , wherein the computation calculates the translational kinetic energy as inversely proportional to the square of the duration and as proportional to the square of the estimate of the integral. 
     
     
       9. The apparatus of  claim 1 , wherein the translational kinetic energy is calculated as a variable that has a range of more than two values. 
     
     
       10. A method of estimating translational kinetic energy of a ball passing through an aperture in a net, which net includes one or more cords that are stretchable, electrically conductive and have an electrical resistance that varies depending on the extent to which one or more cords are stretched, which method comprises, in combination:
 (a) measuring the electrical resistance by at least one sensor; and 
 (b) performing a computation by at least one processor, which computation includes
 (i) calculating a duration of a time period, which period starts when the electrical resistance exceeds a baseline plus a first amount and ends when the electrical resistance is less than the baseline minus a second amount, and 
 (ii) calculating, based at least in part on the duration of the time period, the translational kinetic energy of the ball that passes through the aperture in the net, 
 
 wherein the one or more cords are positioned such that the one or more cords stretch when the ball passes through the aperture. 
 
     
     
       11. The method of  claim 10 , wherein the net comprises a basketball net. 
     
     
       12. The method of  claim 10 , wherein the net is tubular. 
     
     
       13. The method of  claim 10 , wherein the computation includes calculating an instantaneous rate of change of the resistance. 
     
     
       14. The method of  claim 10 , wherein the first amount is different than the second amount. 
     
     
       15. The method of  claim 10 , wherein the computation includes a mathematical operation involving a first term that is inversely proportional to the square of the duration. 
     
     
       16. The method of  claim 10 , wherein the computation also includes:
 (a) calculating an estimate of an integral of change in the resistance, by calculating a sum of samples; and 
 (b) calculating the translational kinetic energy as proportional to the square of the estimate of the integral. 
 
     
     
       17. The method of  claim 16 , wherein the computation calculates the translational kinetic energy as inversely proportional to the square of the duration and as proportional to the square of the estimate of the integral. 
     
     
       18. The method of  claim 10 , wherein only one measurement of the resistance is taken at any given time. 
     
     
       19. The method of  claim 10 , wherein the resistance increases as stretch of the one or more cords increases. 
     
     
       20. The method of  claim 10 , wherein the translational kinetic energy is calculated as a variable that has a range of more than two values.